The coefficient of friction is often a crucial parameter for the control of driver assistance systems, such as e.g. anti-skid systems (ABS), traction control systems (ASR) or electronic stability programs (ESP) in all kind of vehicles. For such systems which are integrated in the vehicle, it is valuable to know at which actual values of the slip of the individual tire the friction is best utilized under all different driving conditions, i.e. during constant driving, accelerating and braking both at longitudinal and turning movements of the vehicle. The actual value of friction can be also communicated to the driver in order to provide him with information which driving style will be adequate.
It is well known that the tires of a vehicle are exposed to slip, which occurs due to the difference between the vehicle speed and the rotational speed of the single wheels, when forces between the tires and the road surface have to be transferred during driving. In addition to this longitudinal slip, lateral slip occurs when the tire is moving perpendicular to the rotational direction.
In this context, much effort still is spent on developing algorithms for the estimation of different parameters relating to a tire-to-road contact and/or a relation between a wheel and a vehicle motion, in particular for the estimation of the coefficient of friction, a parameter which cannot be measured or sensed directly during driving.
In recent developments, in general, when dealing with the dynamics in vehicles and the control of the forces to be developed by the tire, recursive estimation algorithms are used which mainly are based on the common assumption that the tire forces can be expressed by a nonlinear function which is dependent on the slip and in addition on a set of parameters which describe the actual conditions of the tire and the road surface.
Such approaches take into account that the tire force which is developed at a particular slip substantially depends on other factors, such as tire pressure, tire temperature, tire load etc., whereby different models have been developed in order to describe the parameter-dependent behaviour and relations. Other signals to be used in such algorithms include the wheel speed, the vehicle speed, the engine torque, longitudinal and lateral accelerations of the vehicle, vehicle yaw rate etc.
In general, parameters related to the vehicle motion may include all kind of motions, forces and torques acting on and in the vehicle as well as on the individual wheels.
For example, concerning the determination of the coefficient of friction, European patent EP 0 630 786 B1 suggests a method, in which the wheel speed, the rotational acceleration of the vehicle wheel and the braking pressure are determined, the wheel slip is calculated therefrom and from these values the coefficient of friction is determined by means of linear recursive estimation algorithms.
One well-known approach is based on the estimation of the tire stiffness, which can be described by the inclination of the tire force relative to the tire slip at low slips. From the value of the inclination it is distinguished between different conditions of the road surface by using a linear tire model which assumes that the actual tire stiffness and the actual road condition are interrelated.
However, the tire stiffness depends on many factors and a generic relation between the inclination and the exact coefficient of friction or other parameters relating to a tire-to-road contact and/or a relation between a wheel and a vehicle motion is therefore not possible to obtain. Even the surface detection is not always reliable due to the large variation of the tire stiffness invoked by other reasons. Thus, the use of the tire stiffness as an indicator for friction, other tire-dependent or other vehicle motion-dependent parameters is limited to certain, few real conditions. This is particular due to the fact that the parameters used for the algorithms in question can change quickly so that also the importance of each particular parameter changes as the value of, e.g. the slip changes. In some scenarios, the curvature of the relation between the tire force and the tire slip might be misinterpreted as a changed value of the tire stiffness for higher tire forces.